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The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Simply stated, floating-point algebra is algebra performed on floating-point representations by any number of automated devices. Traditionally, this definition is phrased so ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

The hyperbolic cosine is defined as coshz=1/2(e^z+e^(-z)). (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

By way of analogy with the usual tangent tanz=(sinz)/(cosz), (1) the hyperbolic tangent is defined as tanhz = (sinhz)/(coshz) (2) = (e^z-e^(-z))/(e^z+e^(-z)) (3) = ...